{"title":"边边角三角形同余公理与完全四边形","authors":"P. Csiba, L. Németh","doi":"10.3934/era.2023065","DOIUrl":null,"url":null,"abstract":"Among the triangle congruence axioms, the side-side-angle (SsA) axiom states that two triangles are congruent if and only if two pairs of corresponding sides and the angles opposite the longer sides are equal. We construct two triangle sequences in which the items satisfy a modified condition. We require that the opposite angles of the shorter sides be equal. The locus of the intersection points of other sides of triangles is derived to be a hyperbola, and in a generalized form defined by a complete quadrilateral, it is a conic section.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Side-side-angle triangle congruence axiom and the complete quadrilaterals\",\"authors\":\"P. Csiba, L. Németh\",\"doi\":\"10.3934/era.2023065\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Among the triangle congruence axioms, the side-side-angle (SsA) axiom states that two triangles are congruent if and only if two pairs of corresponding sides and the angles opposite the longer sides are equal. We construct two triangle sequences in which the items satisfy a modified condition. We require that the opposite angles of the shorter sides be equal. The locus of the intersection points of other sides of triangles is derived to be a hyperbola, and in a generalized form defined by a complete quadrilateral, it is a conic section.\",\"PeriodicalId\":48554,\"journal\":{\"name\":\"Electronic Research Archive\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Research Archive\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/era.2023065\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Research Archive","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/era.2023065","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Side-side-angle triangle congruence axiom and the complete quadrilaterals
Among the triangle congruence axioms, the side-side-angle (SsA) axiom states that two triangles are congruent if and only if two pairs of corresponding sides and the angles opposite the longer sides are equal. We construct two triangle sequences in which the items satisfy a modified condition. We require that the opposite angles of the shorter sides be equal. The locus of the intersection points of other sides of triangles is derived to be a hyperbola, and in a generalized form defined by a complete quadrilateral, it is a conic section.